Study of ∧ Hypernuclei Using the Beyond-mean-field Approach with Skyrme-type N∧ Interaction

The beyond-mean-field Skyrme-Hartree-Fock approach is adopted to investigate the properties of _∧⁹Be, _∧∧¹⁰Be, _∧¹³C and _∧²¹Ne. The nucleon-nucleon (NN) interaction SLy4 and the nucleon-hyperon(N∧) interaction Skyrme-type SLL4 are used. The spin-orbit force of hyperon is included to show the spin-orbit splitting and non-crossing effect with BCS method to deal with pairing force. Energies of different configurations, such as ¹²C⊗∧0001/2⁺, ¹²C⊗∧1101/2^-, ¹²C⊗∧1013/2^-, ¹²C⊗∧1011/2^-, ⁸Be⊗∧0001/2⁺, ⁸Be⊗∧1101/2^-, 8 Be⊗∧1013/2^- and ⁸Be⊗∧1011/2^- are given and used to study the effects of ∧ occupying different orbitals. The calculated energy spectra, including both positive-and negative-parity levels, are given and compared to the experimental data. The observed positive-parity spin-doublet (3/2⁺,5/2⁺) are successfully reproduced, but the energy difference needs further investigation. The two well known band structures corresponding to the genuine hypernuclear states and the ⁹Be-analog states are also obtained and compared with the observed ones. The shrinkage effect of ∧ occupying ∧0001/2⁺ is investigated through the density distributions of nuclear core. And finally the calculation results of _∧²¹Ne are given and compared with the results of RMF method, which are nearly the same but with differences in some details.